223:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento espacial:@0.733496:0.043660:0.926913:0.043660:0.926913:0.024915:0.733496:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Evaluación formativa:@0.131433:0.098522:0.446328:0.098522:0.446328:0.067281:0.131433:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Las rectas:@0.073089:0.140040:0.178761:0.140040:0.178761:0.123370:0.073089:0.123370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.178798:0.140040:0.225162:0.140040:0.225162:0.123356:0.178798:0.123356:0.000000:0.000000:0.000000:0.000000 y son paralelas. Si 2 72º, halla el :@0.197588:0.140040:0.489656:0.140040:0.489656:0.123370:0.197588:0.123370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∡ =:@0.356664:0.140622:0.396847:0.140622:0.396847:0.122968:0.356664:0.122968:0.000000:0.000000:0.000000 valor de los ángulos pedidos y da una justificación :@0.103196:0.156682:0.489746:0.156682:0.489746:0.140012:0.103196:0.140012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de cómo se halló el valor.:@0.103196:0.173323:0.293070:0.173323:0.293070:0.156654:0.103196:0.156654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4:@0.166931:0.275170:0.173464:0.275170:0.173464:0.263743:0.166931:0.263743:0.000000 3:@0.194388:0.272457:0.200921:0.272457:0.200921:0.261030:0.194388:0.261030:0.000000 5:@0.305621:0.204337:0.312154:0.204337:0.312154:0.192909:0.305621:0.192909:0.000000 6:@0.334350:0.201230:0.340883:0.201230:0.340883:0.189803:0.334350:0.189803:0.000000 1:@0.164990:0.251720:0.171523:0.251720:0.171523:0.240293:0.164990:0.240293:0.000000 2:@0.194388:0.248291:0.200921:0.248291:0.200921:0.236864:0.194388:0.236864:0.000000 8:@0.310468:0.226193:0.317001:0.226193:0.317001:0.214765:0.310468:0.214765:0.000000 7:@0.337804:0.222905:0.344337:0.222905:0.344337:0.211477:0.337804:0.211477:0.000000 m:@0.192435:0.204434:0.206140:0.204434:0.206140:0.190149:0.192435:0.190149:0.000000 p:@0.406297:0.190432:0.415535:0.190432:0.415535:0.176148:0.406297:0.176148:0.000000 n:@0.330108:0.190432:0.339078:0.190432:0.339078:0.176148:0.330108:0.176148:0.000000 a. :@0.104633:0.340762:0.120076:0.340762:0.120076:0.325049:0.104633:0.325049:0.000000:0.000000:0.000000 ∡:@0.134834:0.341344:0.150167:0.341344:0.150167:0.323690:0.134834:0.323690:0.000000 3 :@0.150075:0.340762:0.163015:0.340762:0.163015:0.325049:0.150075:0.325049:0.000000:0.000000 b. :@0.104633:0.372125:0.121531:0.372125:0.121531:0.356413:0.104633:0.356413:0.000000:0.000000:0.000000 ∡:@0.134834:0.372708:0.150167:0.372708:0.150167:0.355054:0.134834:0.355054:0.000000 6 :@0.150075:0.372125:0.163015:0.372125:0.163015:0.356413:0.150075:0.356413:0.000000:0.000000 c. :@0.104633:0.403490:0.119708:0.403490:0.119708:0.387777:0.104633:0.387777:0.000000:0.000000:0.000000 ∡:@0.134834:0.404073:0.150167:0.404073:0.150167:0.386418:0.134834:0.386418:0.000000 5 :@0.150075:0.403490:0.163015:0.403490:0.163015:0.387777:0.150075:0.387777:0.000000:0.000000 d. :@0.104633:0.434854:0.121512:0.434854:0.121512:0.419141:0.104633:0.419141:0.000000:0.000000:0.000000 ∡:@0.134834:0.435436:0.150167:0.435436:0.150167:0.417782:0.134834:0.417782:0.000000 8 :@0.150075:0.434854:0.163015:0.434854:0.163015:0.419141:0.150075:0.419141:0.000000:0.000000 e. :@0.104633:0.466217:0.120445:0.466217:0.120445:0.450505:0.104633:0.450505:0.000000:0.000000:0.000000 ∡:@0.134834:0.466800:0.150167:0.466800:0.150167:0.449145:0.134834:0.449145:0.000000 4 :@0.150075:0.466217:0.163015:0.466217:0.163015:0.450505:0.150075:0.450505:0.000000:0.000000 2. Si se sabe que las rectas y son paralelas, halla el :@0.073089:0.493580:0.489739:0.493580:0.489739:0.476911:0.073089:0.476911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.284268:0.493580:0.323825:0.493580:0.323825:0.477174:0.284268:0.477174:0.000000:0.000000:0.000000 valor de los ángulos y .:@0.103196:0.510222:0.300245:0.510222:0.300245:0.493553:0.103196:0.493553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.257890:0.510805:0.296527:0.510805:0.296527:0.493150:0.257890:0.493150:0.000000:0.000000:0.000000 :@0.303121:0.550524:0.325085:0.550524:0.325085:0.536481:0.303121:0.536481:0.000000:0.000000 10°:@0.325085:0.550061:0.343680:0.550061:0.343680:0.537562:0.325085:0.537562:0.000000:0.000000:0.000000 :@0.235036:0.550524:0.253002:0.550524:0.253002:0.536481:0.235036:0.536481:0.000000:0.000000 15°:@0.253880:0.550061:0.274232:0.550061:0.274232:0.537562:0.253880:0.537562:0.000000:0.000000:0.000000 64°:@0.262856:0.613923:0.281451:0.613923:0.281451:0.601424:0.262856:0.601424:0.000000:0.000000:0.000000 m:@0.411507:0.549181:0.424698:0.549181:0.424698:0.535432:0.411507:0.535432:0.000000 p:@0.303063:0.531234:0.311953:0.531234:0.311953:0.517485:0.303063:0.517485:0.000000 n:@0.416065:0.632716:0.424698:0.632716:0.424698:0.618967:0.416065:0.618967:0.000000 α:@0.117801:0.680717:0.129048:0.680717:0.129048:0.663062:0.117801:0.663062:0.000000 :@0.265562:0.690884:0.293339:0.690884:0.293339:0.675172:0.265562:0.675172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.301908:0.680717:0.313155:0.680717:0.313155:0.663062:0.301908:0.663062:0.000000 3. Si se sabe que las rectas y son paralelas, halla el :@0.073089:0.718246:0.489739:0.718246:0.489739:0.701577:0.073089:0.701577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.284268:0.718246:0.323825:0.718246:0.323825:0.701840:0.284268:0.701840:0.000000:0.000000:0.000000 valor de los ángulos y .:@0.103196:0.734888:0.300245:0.734888:0.300245:0.718219:0.103196:0.718219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.257890:0.735471:0.296527:0.735471:0.296527:0.717817:0.257890:0.717817:0.000000:0.000000:0.000000 :@0.254284:0.875174:0.265445:0.875174:0.265445:0.859125:0.254284:0.859125:0.000000 :@0.259036:0.850930:0.285141:0.850930:0.285141:0.834880:0.259036:0.834880:0.000000:0.000000 40°:@0.285141:0.850400:0.308401:0.850400:0.308401:0.836116:0.285141:0.836116:0.000000:0.000000:0.000000 6:@0.294562:0.799731:0.302728:0.799731:0.302728:0.785447:0.294562:0.785447:0.000000 :@0.302728:0.800260:0.313890:0.800260:0.313890:0.784211:0.302728:0.784211:0.000000 m:@0.430376:0.777981:0.445451:0.777981:0.445451:0.762268:0.430376:0.762268:0.000000 p:@0.210833:0.887720:0.220993:0.887720:0.220993:0.872007:0.210833:0.872007:0.000000 n:@0.435585:0.873449:0.445451:0.873449:0.445451:0.857737:0.435585:0.857737:0.000000 α:@0.117801:0.923253:0.129048:0.923253:0.129048:0.905598:0.117801:0.905598:0.000000 :@0.265562:0.933420:0.293339:0.933420:0.293339:0.917707:0.265562:0.917707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.301908:0.923252:0.313155:0.923252:0.313155:0.905598:0.301908:0.905598:0.000000 4. Si se sabe que las rectas y son paralelas, halla el :@0.514231:0.136836:0.930863:0.136836:0.930863:0.120167:0.514231:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n :@0.725667:0.136836:0.768537:0.136836:0.768537:0.120430:0.725667:0.120430:0.000000:0.000000:0.000000:0.000000 valor de los ángulos y .:@0.544337:0.153478:0.741386:0.153478:0.741386:0.136808:0.544337:0.136808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.699031:0.154061:0.737668:0.154061:0.737668:0.136406:0.699031:0.136406:0.000000:0.000000:0.000000 :@0.703292:0.288213:0.714453:0.288213:0.714453:0.272163:0.703292:0.272163:0.000000 m:@0.871517:0.196569:0.886593:0.196569:0.886593:0.180856:0.871517:0.180856:0.000000 p:@0.651974:0.306308:0.662135:0.306308:0.662135:0.290595:0.651974:0.290595:0.000000 n:@0.876727:0.292038:0.886593:0.292038:0.886593:0.276325:0.876727:0.276325:0.000000 3:@0.612780:0.286977:0.620946:0.286977:0.620946:0.272693:0.612780:0.272693:0.000000 :@0.620946:0.287507:0.647051:0.287507:0.647051:0.271457:0.620946:0.271457:0.000000:0.000000 10°:@0.647051:0.286977:0.668303:0.286977:0.668303:0.272693:0.647051:0.272693:0.000000:0.000000:0.000000 5:@0.747354:0.196254:0.755520:0.196254:0.755520:0.181970:0.747354:0.181970:0.000000 :@0.756524:0.196783:0.777056:0.196783:0.777056:0.180734:0.756524:0.180734:0.000000:0.000000 10°:@0.778060:0.196254:0.801320:0.196254:0.801320:0.181970:0.778060:0.181970:0.000000:0.000000:0.000000 α:@0.558942:0.341842:0.570189:0.341842:0.570189:0.324188:0.558942:0.324188:0.000000 :@0.706704:0.352009:0.734480:0.352009:0.734480:0.336296:0.706704:0.336296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.743050:0.341842:0.754297:0.341842:0.754297:0.324188:0.743050:0.324188:0.000000 5. Si se sabe que las rectas y son paralelas, halla el :@0.514231:0.379372:0.930880:0.379372:0.930880:0.362702:0.514231:0.362702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n:@0.725409:0.379372:0.764966:0.379372:0.764966:0.362966:0.725409:0.362966:0.000000:0.000000:0.000000 valor de los ángulos y .:@0.544337:0.396014:0.741386:0.396014:0.741386:0.379344:0.544337:0.379344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.699031:0.396596:0.737668:0.396596:0.737668:0.378942:0.699031:0.378942:0.000000:0.000000:0.000000 m:@0.871517:0.439105:0.886593:0.439105:0.886593:0.423392:0.871517:0.423392:0.000000 p:@0.619651:0.548844:0.629812:0.548844:0.629812:0.533131:0.619651:0.533131:0.000000 q:@0.810461:0.548844:0.820437:0.548844:0.820437:0.533131:0.810461:0.533131:0.000000 n:@0.876727:0.534574:0.886593:0.534574:0.886593:0.518861:0.876727:0.518861:0.000000 4:@0.783283:0.512146:0.791449:0.512146:0.791449:0.497862:0.783283:0.497862:0.000000 :@0.791449:0.512676:0.802611:0.512676:0.802611:0.496626:0.791449:0.496626:0.000000 5:@0.791432:0.438922:0.799599:0.438922:0.799599:0.424638:0.791432:0.424638:0.000000 :@0.799599:0.439452:0.810760:0.439452:0.810760:0.423402:0.799599:0.423402:0.000000 2:@0.643254:0.533364:0.651420:0.533364:0.651420:0.519080:0.643254:0.519080:0.000000 :@0.651420:0.533894:0.662582:0.533894:0.662582:0.517845:0.651420:0.517845:0.000000 140°:@0.628311:0.438796:0.660741:0.438796:0.660741:0.424512:0.628311:0.424512:0.000000:0.000000:0.000000:0.000000 α:@0.558942:0.584377:0.570189:0.584377:0.570189:0.566723:0.558942:0.566723:0.000000 :@0.706704:0.594545:0.734480:0.594545:0.734480:0.578832:0.706704:0.578832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.743050:0.584377:0.754297:0.584377:0.754297:0.566723:0.743050:0.566723:0.000000 6. Halla el valor de los ángulos y si las rectas y :@0.514231:0.621908:0.930815:0.621908:0.930815:0.605238:0.514231:0.605238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α β:@0.757161:0.622490:0.795449:0.622490:0.795449:0.604836:0.757161:0.604836:0.000000:0.000000:0.000000 m n:@0.886988:0.621908:0.926913:0.621908:0.926913:0.605502:0.886988:0.605502:0.000000:0.000000:0.000000 son paralelas, y la recta q es la bisectriz del ángulo :@0.544355:0.638550:0.931101:0.638550:0.931101:0.621880:0.544355:0.621880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∡:@0.544355:0.655774:0.559688:0.655774:0.559688:0.638120:0.544355:0.638120:0.000000 SET:@0.559596:0.655192:0.583747:0.655192:0.583747:0.638785:0.559596:0.638785:0.000000:0.000000:0.000000 .:@0.583692:0.655192:0.587502:0.655192:0.587502:0.638522:0.583692:0.638522:0.000000 :@0.552638:0.811639:0.556541:0.811639:0.556541:0.794969:0.552638:0.794969:0.000000 m:@0.873428:0.710890:0.888504:0.710890:0.888504:0.695177:0.873428:0.695177:0.000000 p:@0.644295:0.808023:0.654456:0.808023:0.654456:0.792310:0.644295:0.792310:0.000000 q:@0.632089:0.783945:0.642066:0.783945:0.642066:0.768232:0.632089:0.768232:0.000000 E:@0.682764:0.778564:0.691342:0.778564:0.691342:0.762852:0.682764:0.762852:0.000000 S:@0.799025:0.786691:0.807566:0.786691:0.807566:0.770978:0.799025:0.770978:0.000000 T:@0.684476:0.738277:0.693036:0.738277:0.693036:0.722564:0.684476:0.722564:0.000000 n:@0.856713:0.769217:0.866579:0.769217:0.866579:0.753504:0.856713:0.753504:0.000000 :@0.694025:0.709338:0.705186:0.709338:0.705186:0.693289:0.694025:0.693289:0.000000 2:@0.659419:0.760764:0.667585:0.760764:0.667585:0.746480:0.659419:0.746480:0.000000 :@0.667585:0.761293:0.678747:0.761293:0.678747:0.745244:0.667585:0.745244:0.000000 25°:@0.736495:0.760575:0.759755:0.760575:0.759755:0.746290:0.736495:0.746290:0.000000:0.000000:0.000000 α:@0.558942:0.843554:0.570189:0.843554:0.570189:0.825900:0.558942:0.825900:0.000000 :@0.706704:0.853721:0.734480:0.853721:0.734480:0.838008:0.706704:0.838008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.743050:0.843554:0.754297:0.843554:0.754297:0.825900:0.743050:0.825900:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000